Gauss映射对曲面的影响

摘要

Gauss映射用来描述曲面的弯曲性非常直观，也用来说明高斯曲率的几何意义，利用高斯映射象的讨论可以探讨曲面的1些性质．文章以局部曲面的基本理论为基础，通过对曲面的渐近曲线、曲面上 任意两方向的夹角和可展曲面的高斯映射象的讨论来说明高斯（Gauss）映射对曲面的影响．

关键词：高斯（Gauss）映射；渐近曲线；高斯曲率；可展曲面；正螺面

ABSTRACT

Gauss mipping is used to describe the bending of surface very visual,used to illustrate the geometric properties of Gauss curvature too.As the use of Gauss mipping image,we can discuss some surface’s properties.This paper on basis of surface’s local principle.Through discussing the Gauss mipping image of the surface’s asymptotic curve and the camber between any two directions of surface and the developable surface to illustrate the impact on surface of Gauss mipping.

Keywords: Gauss mipping;asymptotic curve;Gauss curvature;developable surface;right helicoid

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